I know say G-reg to N-reg needs an Export CofA which is basically an Annual.
This can be avoided if you have a letter from the original certification agency (the DGAC if it is a TB20, for example) stating that the aircraft complied with FAA requirements when originally made. No, don’t ask me how this works. The FAA DAR accepts that letter directly.
What about say F-reg to D-reg, G-reg to PH-reg, etc. Is the process the same?
The process for intra-EASA is very simple. If the aircraft has a valid ARC, it is a pure paper exercise. For the UK CAA, all you have to do is fill out a simple form and submit a confirmation letter from the previous CAA that the aircraft was deregistered. That serves as proof that it was actually on that register. The aircraft never has to fly to the UK or needs to see any UK inspector.
I guess other CAAs require slightly differente paperwork but that’s basically the process.
When I was transfering PH-VMV to 9A-SAW Croatian CAA just took current ARC crossed old registration, wrote new one and put agency’s signature and stamp below new reg. They issued new CofR, noise certificate and telecommunication agency issued new radio licence. Everything was done in few days.
It’s generally straightforward, but problems may arise if no aircraft of that particular type have been previously registered in the country of the new registration. After buying G-NODE, I inquired with the Czech CAA about the registration transfer procedures, and since no AA-5Bs had ever lived under OK-reg, the airworthiness department asked me to submit the whole kit of official maintenance documentation for review and approval. So I stayed on G-reg.
Problems may arise even if the type is common in the “new” country of registration. I bought a very common type from another EASA country and when attempting to change to G reg I eventually gave up because of all the changes required by our CAA and the cost of so doing. I gave up after spending several thousands of pounds on pure paperwork (yes seriously not a single penny had been spent on engineering at that time) and my engineer estimated the cost of the CAA requirements in excess of £30k. Needless to say a very quick discussion ensued with the “old” country of registration to which the aircraft was promptly returned with the original registration and also because the aircraft had not been flown during the lengthy negotiations with UK CAA the issue of a new C of A and ARC was completed swiftly and with great understanding.
My TB20 was the first one on Croatian registry and I got 3 months to deliver Aircraft Program Manual and additional month to correct it and align it with Agency’s remarks. Of Course Aircraft Maintenance Manual and POH were required to be delivered as well which wasn’t a problem because they are available from Socata in electronic form with no charge. During all these 4 months there was no limitation on flying.
Oddly enough I too looked at transferring my then G-reg TB20 to the Czech OK-reg, almost 10 years ago.
I was looking into this because I am entitled to a Czech passport, and there was a scenario which would have enabled me to avoid the EASA FCL crap, by renouncing my UK passport. That never happened because the wording of some proposal got changed.
Their CAA told me there was no OK-reg TB20 (there are some now, of course) and sent me many hundreds of pages of documentation to comply with. They were also ridiculously strict on some stuff. I left it at that.
You would change citizenship because of your hobby airplane? Now that is truly remarkable!
There is/was no difference in what you can or cannot do with either passport. Both are EU. I can get a Czech passport with just a day spent hanging around the embassy in London; it’s on my list of things to do and could be handy one day.
There was some route (I have forgotten the details) whereby CZ would validate an FAA IR and then you would be “in” the JAA system, and grandfathered onwards. A bit like Hungary (and others) offered albeit via a more convoluted route. This avoided the stupid JAA IR exams and flight training. All old history now.
Nowadays, the only difference is that the UK passport holder’s beheading video will appear on the internet a lot sooner, if he finds himself in the wrong place.
There is/was no difference in what you can or cannot do with either passport. Both are EU.
The UK passport has some advantages: you get visa free travel to Commonwealth countries, India and Australia require a visa with a Czech passport. From an ease of travel point of view, I believe the UK passport is the most convenient in the world. German passport gives much more ransom though in case of kidnapping. UK passport holders get beheaded, Germans traded 
